Helical gears are similar to spur gears except that the gears teeth are at an angle with
the axis of the gears. A helical gear is termed right handed or left handed as determined
by the direction the teeth slope away from the viewer looking at the top gear surface
along the axis of the gear. ( Alternatively if a gear rests on its face the
hand is in the direction of the slope of the teeth) . Meshing helical gears
must be of opposite hand.
Meshed helical gears can be at an angle to each other (up to 90o ). The helical gear
provides a smoother mesh and can be operated at greater speeds than a straight spur gear. In operatation
helical gears generate axial shaft forces in addition to the radial shaft force generated by normal spur gears.

In operation the initial tooth contact of a helical gear is a point which develops into a full line
contact as the gear rotates. This is a smoother cycle than a spur which has an initial line contact. Spur gears
are generally not run at peripheral speed of more than 10m/s. Helical gears can be run at speed exceeding
50m/s when accurately machined and balanced.

Standards ... The same standards apply to helical gears as for spur gears

BS ISO 6336-5:2003..Calculation of load capacity of spur and helical gears. Strength and quality of materials

Helical gear parameters

A helical gear train with parallel axes is very similar to a spur gear with the same tooth
profile and proportions. The primary difference is that the teeth are machined at an
angle to the gear axis.

Helix Angle ..

The helix angle of helical gears β is generally selected from
the range 6,8,10,12,15,20 degrees. The larger the angle the smoother the motion and the
higher speed possible however the thrust loadings on the supporting bearings also
increases.
In case of a double or herringbone gear β
values 25,30,35,40 degrees can also be used. These large angles can be used because the
side thrusts on the two sets of teeth cancel each other allowing larger angles with no penalty

Pitch /module ..

For helical gears the circular pitch is measured in two ways
The traverse circular pitch (p) is the same as for spur gears and is measured along the pitch circle
The normal circular pitch p n is measured normal to the helix of the gear.
The diametric pitch is the same as for spur gears ... P = z g /dg = z p /d p ....d= pitch circle dia (inches).
The module is the same as for spur gears ...
m = dg/z g = d p/z p.... d = pitch circle dia (mm).

Helical Gear geometrical proportions

p = Circular pitch = d g. p / z g = d p. p / z p

p n = Normal circular pitch = p .cosβ

P n =Normal diametrical pitch = P /cosβ

p x = Axial pitch = p c /tanβ

m n =Normal module = m / cosβ

α n = Normal pressure angle = tan -1 ( tanα.cos β )

β =Helix angle

d g = Pitch diameter gear = z g. m

d p = Pitch diameter pinion = z p. m

a =Center distance = ( z p + z g )* m n /2 cos β

a a = Addendum = m

a f =Dedendum = 1.25*m

b = Face width of narrowest gear

Herringbone / double crossed helical gears

Crossed Helical Gears

When two helical gears are used to transmit power between non parallel, non-intersecting
shafts, they are generally called crossed helical gears. These are simply normal
helical gears with non-parallel shafts. For crossed helical gears to operate successfully
they must have the same pressure angle and the same normal pitch. They need not
have the same helix angle and they do not need to be opposite hand.
The contact is not a good line contact as for parallel helical gears and is often little
more than a point contact. Running in crossed helical gears tend to marginally improve
the area of contact.

The relationship between the shaft angles E and the helix angles
β 1 & β2 is as follows

E = (Same Helix Angle) β1
+ β2 ......(Opposite Helix Angle) β1
- β2

For gears with a 90o crossed axis it is obvious that the gears must be the same hand.

The centres distance (a) between crossed helical gears is calculated as follows

a = m * [(z 1 / cos β1)
+ ( z 1 / cos β1 )] / 2

The sliding velocity Vsof crossed helical gears is given by

Vs = (V1 / cos β1 )
= (V 2 / cos β2 )

Strength and Durability calculations for Helical Gear Teeth

Designing helical gears is normally done in accordance with standards the
two most popular series are listed under standards above: The notes below relate
to approximate methods for estimating gear strengths. The methods are really only
useful for first approximations and/or selection of stock gears (ref links below). —
Detailed design of spur and helical gears should best be completed using :

a) Standards.
b) Books are available providing the necessary guidance.
c) Software is also available making the process very easy. A very reasonably priced and easy to use package is
included in the links below (Mitcalc.com)

The determination of the capacity of gears to transfer the required torque for the
desired operating life is completed by determining the strength of the gear teeth in
bending and also the durability i.e of the teeth ( resistance to wearing/bearing/scuffing loads ) .. The equations below are based on methods
used by Buckingham..

Bending

The Lewis formula for spur gears can be applied to helical gears with minor adjustments
to provide an initial conservative estimate of gear strength in bending. This equation should only
be used for first estimates.

σ = Fb / ( ba. m. Y )

Fb = Normal force on tooth = Tangential Force Ft / cos β

σ = Tooth Bending stress (MPa)

ba = Face width (mm)

Y = Lewis Form Factor

m = Module (mm)

When a gear wheel is rotating the gear teeth come into contact with some degree
of impact. To allow for this a velocity factor is introduced into the equation.
This is given by the Barth equation for milled profile gears.

K v = (6,1 + V ) / 6,1

V = the pitch line velocity = PCD.w/2

The Lewis formula is thus modified as follows

σ = K v.Fb / ba. m. Y

The Lewis form factor Y must be determined for the virtual number of teeth z' = z /cos3β
The bending stress resulting should be less than the allowable bending stress Sb
for the gear material under consideration. Some sample values are provide on this page ef Gear Strength Values

Surface Strength

The allowable gear force from surface durability considerations is determined approximately using the simple equation as follows